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A group having an infinite number of elements. Some infinite groups, such as the integers or rationals, are not continuous groups.

The sequence generated by repeated application of a map. The map is said to have a closed orbit if it has a finite number of elements.

Roughly speaking, a matroid is a finite set together with a generalization of a concept from linear algebra that satisfies a natural set of properties for that concept. For ...

Consider the Euler product zeta(s)=product_(k=1)^infty1/(1-1/(p_k^s)), (1) where zeta(s) is the Riemann zeta function and p_k is the kth prime. zeta(1)=infty, but taking the ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

In the plane, the reflection property can be stated as three theorems (Ogilvy 1990, pp. 73-77): 1. The locus of the center of a variable circle, tangent to a fixed circle and ...

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

A finite division algebra is a field.

If r is a root of a nonzero polynomial equation a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the a_is are integers (or equivalently, rational numbers) and r satisfies no ...

The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...